IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4795-d1289070.html
   My bibliography  Save this article

Kibria–Lukman-Type Estimator for Regularization and Variable Selection with Application to Cancer Data

Author

Listed:
  • Adewale Folaranmi Lukman

    (Department of Mathematics, University of North Dakota, Grand Forks, ND 58202, USA)

  • Jeza Allohibi

    (Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia)

  • Segun Light Jegede

    (Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA)

  • Emmanuel Taiwo Adewuyi

    (Department of Statistics, Ladoke Akintola University of Technology, Ogbomoso 212102, Nigeria)

  • Segun Oke

    (Department of Physics, Chemistry and Mathematics, Alabama A&M University, Huntsville, AL 35762, USA)

  • Abdulmajeed Atiah Alharbi

    (Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawara 42353, Saudi Arabia)

Abstract

Following the idea presented with regard to the elastic-net and Liu-LASSO estimators, we proposed a new penalized estimator based on the Kibria–Lukman estimator with L1-norms to perform both regularization and variable selection. We defined the coordinate descent algorithm for the new estimator and compared its performance with those of some existing machine learning techniques, such as the least absolute shrinkage and selection operator (LASSO), the elastic-net, Liu-LASSO, the GO estimator and the ridge estimator, through simulation studies and real-life applications in terms of test mean squared error (TMSE), coefficient mean squared error (βMSE), false-positive (FP) coefficients and false-negative (FN) coefficients. Our results revealed that the new penalized estimator performs well for both the simulated low- and high-dimensional data in simulations. Also, the two real-life results show that the new method predicts the target variable better than the existing ones using the test RMSE metric.

Suggested Citation

  • Adewale Folaranmi Lukman & Jeza Allohibi & Segun Light Jegede & Emmanuel Taiwo Adewuyi & Segun Oke & Abdulmajeed Atiah Alharbi, 2023. "Kibria–Lukman-Type Estimator for Regularization and Variable Selection with Application to Cancer Data," Mathematics, MDPI, vol. 11(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4795-:d:1289070
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4795/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/23/4795/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Murat Genç & M. Revan Özkale, 2021. "Usage of the GO estimator in high dimensional linear models," Computational Statistics, Springer, vol. 36(1), pages 217-239, March.
    2. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 347-355, July.
    3. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    4. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huang, Lele & Zhao, Junlong & Wang, Huiwen & Wang, Siyang, 2016. "Robust shrinkage estimation and selection for functional multiple linear model through LAD loss," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 384-400.
    2. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    3. Sophie Lambert-Lacroix & Laurent Zwald, 2016. "The adaptive BerHu penalty in robust regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 487-514, September.
    4. Florian Ziel, 2015. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes," Papers 1502.06557, arXiv.org, revised Dec 2015.
    5. T. Cai & J. Huang & L. Tian, 2009. "Regularized Estimation for the Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 65(2), pages 394-404, June.
    6. Jonathan Boss & Alexander Rix & Yin‐Hsiu Chen & Naveen N. Narisetty & Zhenke Wu & Kelly K. Ferguson & Thomas F. McElrath & John D. Meeker & Bhramar Mukherjee, 2021. "A hierarchical integrative group least absolute shrinkage and selection operator for analyzing environmental mixtures," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    7. Ziel, Florian, 2016. "Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR–ARCH type processes," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 773-793.
    8. Qingguo Tang & R. J. Karunamuni, 2018. "Robust variable selection for finite mixture regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 489-521, June.
    9. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.
    11. Abdul Wahid & Dost Muhammad Khan & Ijaz Hussain, 2017. "Robust Adaptive Lasso method for parameter’s estimation and variable selection in high-dimensional sparse models," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-17, August.
    12. Barbato, Michele & Ceselli, Alberto, 2024. "Mathematical programming for simultaneous feature selection and outlier detection under l1 norm," European Journal of Operational Research, Elsevier, vol. 316(3), pages 1070-1084.
    13. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    14. Mingqiu Wang & Guo-Liang Tian, 2016. "Robust group non-convex estimations for high-dimensional partially linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 49-67, March.
    15. Li, Mei & Kong, Lingchen, 2019. "Double fused Lasso penalized LAD for matrix regression," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 119-138.
    16. Guan Yu & Yufeng Liu, 2016. "Sparse Regression Incorporating Graphical Structure Among Predictors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 707-720, April.
    17. Fan, Rui & Lee, Ji Hyung & Shin, Youngki, 2023. "Predictive quantile regression with mixed roots and increasing dimensions: The ALQR approach," Journal of Econometrics, Elsevier, vol. 237(2).
    18. Kepplinger, David, 2023. "Robust variable selection and estimation via adaptive elastic net S-estimators for linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 183(C).
    19. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    20. Oxana Babecka Kucharcukova & Jan Bruha, 2016. "Nowcasting the Czech Trade Balance," Working Papers 2016/11, Czech National Bank.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4795-:d:1289070. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.